Food processor: add all ingredients to a food processor and pulse a few times until it starts to form a ball. Remove from the food processor, knead by hand on a lightly floured bench for 5 minutes until smooth. The dough will be reasonably dry but will hold together and form a ball. If the dough is too sticky, add a little more flour, if it's too dry add a bit more olive oil or water
Stand mixer: Add all ingredients into the bowl of a stand mixer and knead using the dough hook for 5 minutes.
By hand: Add the flour and salt to a medium sized mixing bowl and whisk together. Make a well in the centre and add the eggs and olive oil. Use a butter knife to combine the ingredients then tip out onto a lightly floured bench and knead for 5 minutes until smooth.
Step 2: Rest the dough
Cover the dough with a clean tea towel and let rest on the bench for 30 minutes.
Step 3: Roll out the dough
Pasta roller: Split the dough into 4 pieces. Take one piece and use your hands to flatten it into an oval shaped disc, dusting it generously in flour. Set the pasta roller on the thickest setting (this is 7 on my pasta roller) and roll the sheet of pasta through twice. Continue to feed the dough through the pasta roller, gradually reducing the settings so that the dough gets thinner each time. Make sure you dust the dough with flour between each run through - this helps it to go through smoothly. I usually run the dough through once on each setting until I get to setting 2 or 3.
If the dough gets too long to handle, use a sharp knife to cut it in half and continue to roll through.
Once the pasta is as thin as you want it, you can either stop and use this as lasagne sheets or attach the cutter attachment to make spaghetti or fettucine. Dust the pasta sheet in flour again and roll it through.
I like to prepare a baking sheet with a non stick liner or baking paper and lay the cut pasta into little nests while I cut the rest.
By hand: To roll pasta by hand, split the dough into 4 and shape one piece into a flat oval disc as in the previous method.
Place the dough onto a well floured surface and use a rolling pin to roll it out until it is about 1-2mm thin, adding more flour as necessary to stop the dough from sticking.
Once the dough is your desired thickness, flour the dough again and loosely roll it up into a loose, flat cylinder (see image above). Use a long sharp knife to slice the pasta into your desired noodle width. Transfer the cut pasta onto a lined baking sheet and lay the cut pasta into little nests while you cut the rest.
How to cook fresh pasta:
Bring a large pot of salted water to the boil. Drop the pasta nests into the boiling water and stir so that the noodles don't stick together. Cook for 2-4 minutes until the pasta is cooked to your liking. Strain the pasta and serve immediately!
Notes
How to store fresh pasta:Allow the pasta to dry at room temperature for at least 30 minutes and then transfer to an airtight container. Store in the fridge for 1-2 days or freeze for a couple of months. To cook frozen pasta, I just put it in the pot straight from the freezer and cook for 6-8 minutes (6 minutes for spaghetti, 8 minutes for thicker pasta)